theorem Th29: :: MESFUN17:29

for I, J, K being non empty closed_interval Subset of REAL
for f being PartFunc of [:[:RNS_Real,RNS_Real:],RNS_Real:],RNS_Real
for g being PartFunc of [:[:REAL,REAL:],REAL:],REAL
for E being Element of sigma (measurable_rectangles ((sigma (measurable_rectangles (L-Field,L-Field))),L-Field)) st [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g & E = [:[:I,J:],K:] holds
g is E -measurable